Solve for $x$ and $y$ using elimination. $\begin{align*}-4x+6y &= -2 \\ -6x-2y &= -4\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $1$ and the bottom equation by $3$ $\begin{align*}-4x+6y &= -2\\ -18x-6y &= -12\end{align*}$ Add the top and bottom equations. $-22x = -14$ Divide both sides by $-22$ and reduce as necessary. $x = \dfrac{7}{11}$ Substitute $\dfrac{7}{11}$ for $x$ in the top equation. $-4( \dfrac{7}{11})+6y = -2$ $-\dfrac{28}{11}+6y = -2$ $6y = \dfrac{6}{11}$ $y = \dfrac{1}{11}$ The solution is $\enspace x = \dfrac{7}{11}, \enspace y = \dfrac{1}{11}$.